Middle classThe middle class refers to a class of people in the middle of a social hierarchy, often defined by occupation, income, education, or social status. The term has historically been associated with modernity, capitalism and political debate. Common definitions for the middle class range from the middle fifth of individuals on a nation's income ladder, to everyone but the poorest and wealthiest 20%. Theories like "Paradox of Interest" use decile groups and wealth distribution data to determine the size and wealth share of the middle class.
Social classA social class or social stratum is a grouping of people into a set of hierarchical social categories, the most common being the upper, middle and lower classes. Membership in a social class can for example be dependent on education, wealth, occupation, income, and belonging to a particular subculture or social network. "Class" is a subject of analysis for sociologists, political scientists, anthropologists and social historians. The term has a wide range of sometimes conflicting meanings, and there is no broad consensus on a definition of "class".
Social class in the United KingdomThe social structure of the United Kingdom has historically been highly influenced by the concept of social class, which continues to affect British society today. British society, like its European neighbours and most societies in world history, was traditionally (before the Industrial Revolution) divided hierarchically within a system that involved the hereditary transmission of occupation, social status and political influence.
Functional derivativeIn the calculus of variations, a field of mathematical analysis, the functional derivative (or variational derivative) relates a change in a functional (a functional in this sense is a function that acts on functions) to a change in a function on which the functional depends. In the calculus of variations, functionals are usually expressed in terms of an integral of functions, their arguments, and their derivatives.
Total derivativeIn mathematics, the total derivative of a function f at a point is the best linear approximation near this point of the function with respect to its arguments. Unlike partial derivatives, the total derivative approximates the function with respect to all of its arguments, not just a single one. In many situations, this is the same as considering all partial derivatives simultaneously. The term "total derivative" is primarily used when f is a function of several variables, because when f is a function of a single variable, the total derivative is the same as the ordinary derivative of the function.
Dicarboxylic acidIn organic chemistry, a dicarboxylic acid is an organic compound containing two carboxyl groups (). The general molecular formula for dicarboxylic acids can be written as , where R can be aliphatic or aromatic. In general, dicarboxylic acids show similar chemical behavior and reactivity to monocarboxylic acids. Dicarboxylic acids are used in the preparation of copolymers such as polyamides and polyesters. The most widely used dicarboxylic acid in the industry is adipic acid, which is a precursor in the production of nylon.
Functional (mathematics)In mathematics, a functional (as a noun) is a certain type of function. The exact definition of the term varies depending on the subfield (and sometimes even the author). In linear algebra, it is synonymous with linear forms, which are linear mappings from a vector space into its field of scalars (that is, they are elements of the dual space ) In functional analysis and related fields, it refers more generally to a mapping from a space into the field of real or complex numbers.
Fréchet derivativeIn mathematics, the Fréchet derivative is a derivative defined on normed spaces. Named after Maurice Fréchet, it is commonly used to generalize the derivative of a real-valued function of a single real variable to the case of a vector-valued function of multiple real variables, and to define the functional derivative used widely in the calculus of variations. Generally, it extends the idea of the derivative from real-valued functions of one real variable to functions on normed spaces.
Partial derivativeIn mathematics, a partial derivative of a function of several variables is its derivative with respect to one of those variables, with the others held constant (as opposed to the total derivative, in which all variables are allowed to vary). Partial derivatives are used in vector calculus and differential geometry. The partial derivative of a function with respect to the variable is variously denoted by It can be thought of as the rate of change of the function in the -direction.
Gateaux derivativeIn mathematics, the Gateaux differential or Gateaux derivative is a generalization of the concept of directional derivative in differential calculus. Named after René Gateaux, a French mathematician who died at age 25 in World War I, it is defined for functions between locally convex topological vector spaces such as Banach spaces. Like the Fréchet derivative on a Banach space, the Gateaux differential is often used to formalize the functional derivative commonly used in the calculus of variations and physics.
HyperconjugationIn organic chemistry, hyperconjugation (σ-conjugation or no-bond resonance) refers to the delocalization of electrons with the participation of bonds of primarily σ-character. Usually, hyperconjugation involves the interaction of the electrons in a sigma (σ) orbital (e.g. C–H or C–C) with an adjacent unpopulated non-bonding p or antibonding σ* or π* orbitals to give a pair of extended molecular orbitals. However, sometimes, low-lying antibonding σ* orbitals may also interact with filled orbitals of lone pair character (n) in what is termed negative hyperconjugation.
TetrapyrroleTetrapyrroles are a class of chemical compounds that contain four pyrrole or pyrrole-like rings. The pyrrole/pyrrole derivatives are linked by (=(CH)- or -CH2- units), in either a linear or a cyclic fashion. Pyrroles are a five-atom ring with four carbon atoms and one nitrogen atom. Tetrapyrroles are common cofactors in biochemistry and their biosynthesis and degradation feature prominently in the chemistry of life. Some tetrapyrroles form the active core of compounds with crucial biochemical roles in living systems, such as hemoglobin and chlorophyll.
Conjugated systemIn theoretical chemistry, a conjugated system is a system of connected p-orbitals with delocalized electrons in a molecule, which in general lowers the overall energy of the molecule and increases stability. It is conventionally represented as having alternating single and multiple bonds. Lone pairs, radicals or carbenium ions may be part of the system, which may be cyclic, acyclic, linear or mixed. The term "conjugated" was coined in 1899 by the German chemist Johannes Thiele.
Maleic acidMaleic acid or cis-butenedioic acid is an organic compound that is a dicarboxylic acid, a molecule with two carboxyl groups. Its chemical formula is HO2CCH=CHCO2H. Maleic acid is the cis-isomer of butenedioic acid, whereas fumaric acid is the trans-isomer. It is mainly used as a precursor to fumaric acid, and relative to its parent maleic anhydride, maleic acid has few applications. Maleic acid has a heat of combustion of -1,355 kJ/mol., 22.7 kJ/mol higher than that of fumaric acid.
ChromophoreA chromophore is the part of a molecule responsible for its color. The color that is seen by our eyes is the one not absorbed by the reflecting object within a certain wavelength spectrum of visible light. The chromophore is a region in the molecule where the energy difference between two separate molecular orbitals falls within the range of the visible spectrum (or in informal contexts, the spectrum under scrutiny). Visible light that hits the chromophore can thus be absorbed by exciting an electron from its ground state into an excited state.
Systematic reviewA systematic review is a scholarly synthesis of the evidence on a clearly presented topic using critical methods to identify, define and assess research on the topic. A systematic review extracts and interprets data from published studies on the topic, then analyzes, describes, and summarizes interpretations into a refined conclusion. For example, a systematic review of randomized controlled trials is a way of summarizing and implementing evidence-based medicine.
Fumaric acidFumaric acid is an organic compound with the formula HO2CCH=CHCO2H. A white solid, fumaric acid occurs widely in nature. It has a fruit-like taste and has been used as a food additive. Its E number is E297. The salts and esters are known as fumarates. Fumarate can also refer to the C4H2O42− ion (in solution). Fumaric acid is the trans isomer of butenedioic acid, while maleic acid is the cis isomer. It is produced in eukaryotic organisms from succinate in complex 2 of the electron transport chain via the enzyme succinate dehydrogenase.
OzonolysisIn organic chemistry, ozonolysis is an organic reaction where the unsaturated bonds are cleaved with ozone (). Multiple carbon–carbon bond are replaced by carbonyl () groups, such as aldehydes, ketones, and carboxylic acids. The reaction is predominantly applied to alkenes, but alkynes and azo compounds are also susceptible to cleavage. The outcome of the reaction depends on the type of multiple bond being oxidized and the work-up conditions. Detailed procedures have been reported.
